# Numerical modelling of tidal turbines in the vicinity of a weir

### Application to the Eastern Scheldt barrier

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## Abstract

Tidal energy has a large potential to contribute to achieving the sustainability goals in the Netherlands, due to the long coastline and many estuaries. The investment costs for the implementation of offshore tidal energy are however, still a drawback. A possibility to lower the investment costs for tidal energy is to implement tidal energy extraction into existing coastal infrastructure. An example of this is the current pilot project in the Eastern Scheldt barrier where five Tocardo turbines are attached to the barrier's geometry. The flow passing the turbines in the barrier is contracted by the barrier's geometry and the weir of the foundation of the barrier. Deltares executed an environmental impact assessment for the pilot project with a measurement campaign and a computationally expensive but accurate blade resolved numerical model. In this thesis, a cheaper computational model is added to the these assessment tools. To do so, a turbine parameterization is introduced in the finite element model FinLab. The relatively cheaper computational model should make it possible to execute more extensive sets of simulations of the pilot project in the future. FinLab solves the non-hydrostatic three-dimensional incompressible Navies-Stokes equations in an unstructured mesh with an optional moving free-surface. The used meshes are refined in certain areas of complex flow, such as the turbine parameterization, near the bed, the recirculation zone of the weir and the wake of the turbine. An extra source term is added to the Navier-Stokes equations on a chosen number of turbine integration points, to implement the turbine into the mesh. The placement of these integration points in a two-dimensional mesh is rather simple, the integration points are evenly distributed over the diameter of the turbine. In a three-dimensional mesh, a Fibonacci series is used to implement an actuator disc (AD) into the model domain. A benefit of the Fibonacci circle is that each turbine integration point represents a similar area. The force in the turbine integration points is determined by three methods: an actuator disc with a uniform thrust distribution (uniform AD), a rotational averaged actuator disc blade element momentum method (AD-BEM) and a non-rational averaged actuator line blade element momentum method (AL-BEM). In the uniform AD method, a measured thrust force is divided equally over all turbine integration points. In the BEM methods axial and tangential forces are determined for each turbine integration point based on the local flow speed and experimental lift and drag coefficients. With these methods, it is possible to estimate the generated power and thrust by the turbine. A tip-correction is added to the AD-BEM method to achieve accurate results of the simulations. Furthermore, in both the AD-BEM and AL-BEM methods a small actuator disc is applied in the nacelle region to reproduce the nacelle's blockage of the flow. The uniform AD, AD-BEM and AL-BEM parameterizations are validated with measurement data of flume experiments of a single turbine, flume experiments with different turbine-weir geometries and flume experiments with multiple turbines. The combination of these last two sets of experiments does very well represent the situation in the Eastern Scheldt barrier. As stated above, the AD-BEM and AL-BEM methods are able to estimate the turbine performance. The results of the AD-BEM simulations show a relative error of the turbine's generated power of within 20% in comparison with the flume experiments. The accuracy of the thrust fluctuates more. The AD-BEM method shows to be able to accurately estimate the location of optimum power harvesting in a combined turbine-weir geometry. Both the power and thrust accuracy depend on the mesh resolution and the turbine's rotational speed. Accurate results can be obtained by fine-tuning these settings. The AL-BEM method should be able to produce at least similar similar accuracy to the AD-BEM method when it comes to power and thrust. The AL-BEM method in this thesis is however, not yet able to do so. The results of the simulations with the three methods are also compared with time-averaged velocity measurements of the flume experiments. In the near wake, the uniform AD method does not imply any wake rotation. The rotation of the wake is represented accurately in a time-averaged sense by the AD-BEM method. The AL-BEM method adds transient features such as the downstream trailing tip-vortices to the flow. The velocity shear and turbulent eddies in the near wake as caused by the different methods influence the TKE in the near wake and the recovery of the far wake. The uniform AD under-estimates the wake recovery. The extra velocity shear in the AD-BEM method improves the accuracy but still under-estimates the recovery rate. Resolving the transient features of the near wake in the AL-BEM method further improves the accuracy of the wake recovery. In the simulations with the weir, the geometry seems to be dominant and the wake recovery rate is more accurate than in the simulations without the weir. The AD-BEM method is applied to the Eastern Scheldt field case. Five turbines are introduced in a mesh which represents Roompot 7 to 9 in a simplified manner. Due to the simplification of the mesh, the resistance of the barrier on the flow appeared to be too low. Therefore, the simulations are executed with an upstream discharge boundary. This discharge boundary makes the model less useful to estimate the environmental impact of the turbines in the barrier and at the moment not yet an alternative for the blade resolved model by Deltares when it comes to estimating these effects. With the discharge boundary, the AD-BEM model predicts the average thrust over the five turbines with a relative error of 3% and the average power with a relative error of 12%. This is only slightly less accurate than the results by the blade resolved model by Deltares, while the computational costs of the Eastern Scheldt field case simulations are only a fraction of the earlier executed blade resolved simulations by Deltares.